A revised formulation of the COSMO surface-to-atmosphere transfer scheme Matthias Raschendorfer COSMO Offenbach 2009 Matthias Raschendorfer

The surface to atmosphere transfer scheme calculates the flux densities of prognostic model variables at the lower model boundary. Near the surface only turbulent or molecular processes are important: The total effective vertical flux density can be written as: molecular diffusion coefficient effective velocity scale turbulent length scale Above the laminar layer, where molecular diffusion is negligible and It is above the roughness layer, where the surface area function is equal to 1, it is: At the lowest level, where this is valid, it is: roughness length squared surface area index The surface flux density: (only molecular diffusion close to the rigid surface) and can be chosen so that it holds there: von Kaman constant earth roughness layer surfaces normal to local turbulent and molecular flux densities with an area of times the horizontal projection displace ment height roughn ess length turbulent velocity scale COSMO Offenbach 2009 Matthias Raschendorfer

Vertical gradients increase significantly approaching the surface. Therefore the vertical profile of is not linear and can only be determined using further information. Integration yields: transfer layer resistance roughness layer resistance free atmospheric resistance specific roughness length The constant flux layer: In our model we assume that does not change significantly within the transfer layer between the surface and the lowest full model level. constant flux layer turbulent velocity scale COSMO Offenbach 2009 Matthias Raschendorfer

Calculation of the transport resistances: The current scheme in COSMO explicitly considers the roughness layer resistance for scalars: - applying and an effective SAI value for the whole roughness layer - using the laminar length scale and a proper scaling factor so that for, it can be written: The current scheme in COSMO explicitly considers the free atmospheric resistance: - applying a linear -profile between level(top of the roughness layer) and level (top of the lowest model layer) - using the atmospheric heightand the stability parameter it can be written: COSMO Offenbach 2009 Matthias Raschendorfer

laminar layer logarithmic Prandtl- layer profile unstable stable linear interpolated Prandtl layer roughness layer (expon. roughness- layer profile) lowest model main level upper boundary of the lowest model layer lower boundary of the lowest model layer SYNOP station lawn profile Mean GRID box profile Effective velocity scale profile turbulence- scheme no storage capacity Transfer scheme and 2m-values with respect to a SYNOP lawn: Exponential roughness layer profile is valid for the whole grid box, but it is not present at a SYNOP station from turbulence-scheme COSMO Offenbach 2009 Matthias Raschendorfer

correction factor for roughness and laminar effects generalized squared wind shear frequency (including contribution by non turbulent circulations like wake and convection modes) generalized square for Brunt-Väisälä-frequency (including contribution by sub grid scale condensation Richardson flux number generalized square friction velocity generalized buoyancy heat flux vertically constant in transfer layer Monin-Obukhov stability length scale 2*TKE form TKE equilibrium dissipation constant vertical profile functions constant dependent on The revised vertical profile function: COSMO Offenbach 2009 Matthias Raschendorfer

The laminar layer problem: generalized Reynolds number Profile of as a function of or is only given within a level interval with constant parameters. We already applied a constant SAI. But keeps constant only when molecular diffusion is negligible. For a flat surface and neutral stratification it holds: New approximation of the total diffusion coefficient for neutral stratification : comparison with and laminar layer depth evaluation the resistance integral and assumption: New approximation matches pretty well with measurements of as a function of over a plate! COSMO Offenbach 2009 Matthias Raschendorfer

Normalized transition profile for wind speed: according classical measurements form Reichardt 1951 according approximation COSMO Offenbach 2009 Matthias Raschendorfer molecular solution turbulent solution

contribution with pure turbulent profile function contribution for additional laminar correction pure neutral contribution analytically integrable dimensionless resistance and from TKE scheme The general valid resistance: COSMO Offenbach 2009 Matthias Raschendorfer lowest full level

No laminar layer restrictions No specific roughness length values Stability considered through total transfer layer No stability damping by using turbulent solution of next half level Solution consistent with TKE scheme including - generalized shear production - sub grid scale condensation  Implementation already started  Next step is careful diagnostics and verification using COSMO-SC COSMO Offenbach 2009 Matthias Raschendorfer Conclusion and outlook:  Revised resistance formulation:

3D-run mesdat only with model variables Forced correction run with SC version outdat with correction integrals Identical except horizontla operations and w-equation mesdat containing geo.-wind, vert.-wind und tendencies for horizontal advektion Realistic 3D- run (analysis) Forced test run with SC version outdat with similar results compared to compared test run using the 3D-model Basic scheme of advanced SC-diagnostics: COSMO Offenbach 2009 Matthias Raschendorfer or Component testing: outdat or mesdat may contain 3D-corrections and arbitrary measurements (like surface temperature or surface heat fluxes) the model can be forced by.

COSMO Offenbach 2009 Matthias Raschendorfer interpolated measurements free model run starting wit 3D analysis free model run starting with measurements forced with prognostic variables from 3D-run forced with 3D corrections forced with 3D corrections and measured surface temperature forced with 3D corrections and measured surface heat fluxes Stable stratification over snow at Lindenberg Potential temperature profile atmosphere soil Potential temperature profile atmosphere soil too much turbulent mixing

Thank You for attention! COSMO Offenbach 2009 Matthias Raschendorfer

DWD CLM-Training Course 2009

Matthias RaschendorferDWD CLM-Training Course 2009